{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:A3JUNJNQXJ2RJAKXIJHXGLZW23","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"96311a1deaa5a3f594040fe3a5692afbab18261a99ebcaf241099dc037316f6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-10T08:48:44Z","title_canon_sha256":"79b07cde2770998697fa90f42d75d97038225d3630f1175312c69ea9a3162258"},"schema_version":"1.0","source":{"id":"1111.2421","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2421","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2421v3","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2421","created_at":"2026-05-18T03:26:40Z"},{"alias_kind":"pith_short_12","alias_value":"A3JUNJNQXJ2R","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"A3JUNJNQXJ2RJAKX","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"A3JUNJNQ","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:78acab31a0d4035dc8af40931e08c9805d0dde6a05cb73cea5a2b95a0330a60e","target":"graph","created_at":"2026-05-18T03:26:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Thanks to averaging processes and Gamma-convergence techniques, we are able to link a microscopic description of ferromagnetic materials based on spin lattices and their mesoscopic description in the static framework for the three fundamental contributions: exchange, magnetostatic and external field. The results are in accordance with the classical continuous description of ferromagnetic phenomena and justifies it. This work is a seed towards a dynamic description of ferromagnetic materials.","authors_text":"Brigitte Bid\\'egaray-Fesquet (LJK), Quentin Jouet (LJK), St\\'ephane Labb\\'e (LJK)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-10T08:48:44Z","title":"Static ferromagnetic materials: from the microscopic to the mesoscopic scale"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2421","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:370a77b0fe7ecd32b735d71d96d2d9ace7c5d88f35db90c4db17baa1db13199f","target":"record","created_at":"2026-05-18T03:26:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"96311a1deaa5a3f594040fe3a5692afbab18261a99ebcaf241099dc037316f6a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-10T08:48:44Z","title_canon_sha256":"79b07cde2770998697fa90f42d75d97038225d3630f1175312c69ea9a3162258"},"schema_version":"1.0","source":{"id":"1111.2421","kind":"arxiv","version":3}},"canonical_sha256":"06d346a5b0ba75148157424f732f36d6f63c3c69531732ebfac5283c139b1a48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06d346a5b0ba75148157424f732f36d6f63c3c69531732ebfac5283c139b1a48","first_computed_at":"2026-05-18T03:26:40.133229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:40.133229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nP0ECIYi7x6Q+aImvZg4kwcXeTQgDF+eC2JNiwmjFSSRwBbZjPNRwBDhteWy1kcSvqs+vsJGYIu++bi1yH5DDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:40.133784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2421","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:370a77b0fe7ecd32b735d71d96d2d9ace7c5d88f35db90c4db17baa1db13199f","sha256:78acab31a0d4035dc8af40931e08c9805d0dde6a05cb73cea5a2b95a0330a60e"],"state_sha256":"a793b795eb8d57e1caf5fdac16a87be1d91072f8e2944086d043a05a3516fc20"}